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There is no equivalence.
A quart is a measure of volume. 9x9 is a non-specific measure of area. The two measure different things and, according to basic principles of dimensional analysis, conversion from one to the other is not valid without some addition information.
The casserole measure is non-specific because the question does not specify whether it is 9 in x 9 in, or 9 cm x 9 cm (unlikely) or 9 dm x 9 dm.
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